The relation between the emissive and absorptive power of a body is given by-

Explanation:

Kirchhoff’s law:

• Let E be the total emissive power of the body and α be the absorptivity of the body.
• Emissivity (ϵ) is the ratio of the emissive power of a non-black body to the black body.
• ϵ = \(\frac{E}{E_b}\)
• Kirchhoff’s law also holds for monochromatic radiation, for which
• \(\frac{{{E_{\lambda 1}}}}{{{\alpha _{\lambda 1}}}} = \frac{{{E_{\lambda 2}}}}{{{\alpha _{\lambda 2}}}} = \frac{{{E_{b\lambda }}}}{{{\alpha _{b\lambda }}}} = \frac{{{E_{b\lambda }}}}{1}\)
• ∵ The absorptivity of a black body is one.
• \(\therefore \frac{{{E_\lambda }}}{{{\alpha _\lambda }}} = {E_{b\lambda }} \Rightarrow {\alpha _\lambda } = \frac{{{E_\lambda }}}{{{E_{b\lambda }}}} = {\epsilon_\lambda }\)
• Therefore, the monochromatic emissivity of a black body is equal to the monochromatic absorptivity at the same wavelength.
• Eλ = αλEbλ
• According to Kirchhoff’s law, the ratio of total emissive power to absorptivity is constant for all bodies which are in thermal equilibrium with the surroundings. Therefore, it means that the emissivity of a body is equal to its absorptivity.

Stefan-Boltzmann Law

• The thermal energy radiated by a black body per second per unit area is proportional to the fourth power of the absolute temperature and is given by:
• E ∝ T4
• E = σT4
• σ = The Stefan – Boltzmann constant = 5.67 × 10-8 Wm-2K-4

Wien’s displacement law

• For a black body emissive spectrum, the wavelength λmax giving the maximum emissive power at a temperature is inversely proportional to the absolute temperature.
• λmax = \(\frac{c}{T}\)
• λmaxT= c
• Wavelength = \(\frac{Speed ~of ~Light}{Frequency}\) ⇒ λ = \(\frac{c}{V}\)
•